1. Field of the Invention
The present invention relates to adaptive line enhancers, and to methods for adaptive line enhancement. Applications for the invention lie in the fields of radar, sonar, communications and other related disciplines where digital signal processing may be required.
2. Description of the Related Art
Detection of sinusoidal signals immersed in noise is a fundamental problem in signal processing. The retrieval of sinusoidal or other narrow-band signals which may have been significantly attenuated, frequency shifted because of Doppler effects and corrupted by interference and noise, has conventionally been carried out using analysis of the signal in the frequency domain. This requires the input signal to be Fourier transformed. Once the signal has been Fourier transformed, the strongest spectral component can be detected and a filter designed to either enhance or reject this frequency. For the detection of sinusoids with time-varying frequencies, a Fourier transform with sliding windows can be used. Despite the availability of algorithms, such as the fast Fourier transform (FFT) which are computationally efficient when compared to a direct implementation of the discrete Fourier transform, the frequency domain analysis of the input signal is still relatively inefficient when compared to adaptive line enhancement techniques.
Adaptive line enhancement is an alternative technique to frequency domain analysis based on FFTs. It has been shown (B. Widrow and S. D. Stearns, “Adaptive Signal Processing”, Prentice-Hall, 1985) that Adaptive Line Enhancers (ALEs) require fewer computations than FFT-based techniques and, in certain circumstances, can be more sensitive detectors of sinusoids. The ALE consists of a filter, and an adaptation rule for changing some feature of the filter's frequency response characteristics. Various combinations of filters and adaptation rules have been proposed, with the most recently reported embodiments comprising a lattice Gray-Markel adaptive notch filter and adaptation rules based on a simplified gradient technique (N. I. Cho, C.-H. Choi and S. U. Lee, “Adaptive Line Enhancement by Using an IIR Lattice Notch Filter,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, April 1989; P. A. Regalia, “An Improved Lattice-Based Adaptive IIR Notch filter,” IEEE Trans. Signal Processing, vol. 39, pp. 2124-2128, September 1991). It has been shown that such ALEs provide better convergence to the frequency of interest than previous designs and, in addition, are less sensitive to the finite word length effects which occur in any digital processor.
The transfer function of the Gray-Markel lattice notch filter is expressed as:                               H          lattice                =                                            N              ⁡                              (                z                )                                                    D              ⁡                              (                z                )                                              =                                    (                                                1                  +                  α                                2                            )                        ⁢                                          1                +                                  2                  ⁢                                      k                    0                                    ⁢                                      z                                          -                      1                                                                      +                                  z                                      -                    2                                                                              1                +                                                                            k                      0                                        ⁡                                          (                                              1                        +                        α                                            )                                                        ⁢                                      z                                          -                      1                                                                      +                                  α                  ⁢                                                                           ⁢                                      z                                          -                      2                                                                                                                              (                  Equation          ⁢                                           ⁢          A                )            where k0 determines the notch frequency and where α determines the bandwidth. The notch frequency determining variable k0 should converge to −cos (ω0) to reject a sinusoid with frequency ω0. This filter has zeros on the unit circle at z0=e±ω0, where ω0=cos−1(−k0). The −3 dB attenuation bandwidth BW of the magnitude response of the Gray-Markel lattice notch filter is determined by the following equation:   BW  =            cos              -        1              ⁡          (                        2          ⁢          α                          1          +                      α            2                              )      
A slight gain correction of   (            1      +      α        2    )is needed to achieve unity gain in the passband.
The bandwidth and the notch frequency can be controlled separately by changing k0 and α. This filter structure can easily be implemented using either a direct form realization or a lattice filter structure based on wave digital filters (WDFs) (A. Fettweis and H. Levin and A. Sedlmeyer, “Wave Digital Lattice Filters,” Int. J. Circuit Theory Applicat, vol. 2, no. 2, pp. 203-211, June 1974; A. Fettweis, “Wave Digital Lattice Filters: Theory and practice (invited paper),” Proc. IEEE, vol. 74, pp. 270-327, February 1986).
Referring to FIG. 1, there is shown a block diagram showing functional elements for implementing a known wave digital filter realization of the Gray-Markel notch filter response, the transfer function of which is given in Equation A.
In FIG. 1, there is shown an input 110, a first dynamic adapter block 120, a second dynamic adapter block 130, a summing block 140, an amplifier block 150, an output 160, a notch bandwidth determining block 170 and a notch frequency determining block 180.
An input signal 110 is fed to a first input of the summing block 140 and to a first input of the first dynamic adapter block 120. A first output of the first dynamic adapter block 120 is fed to a second input of the summing block 140. The output of the summing block 140, comprising the result of the addition of input 110 and a first output of the first dynamic adapter block 120, is fed to the input of the amplifier block 150. The amplifier block 150 has a fixed amplitude gain of 0.5. This gain is achieved by a bit-shift operation, and thus, does not require a multiplier. The output of the amplifier block 150 becomes the output signal 160.
A second output of the first dynamic adapter block 120 is left unconnected. A third output of the first dynamic adapter block 120 is fed to a first input of the second dynamic adapter block 130, said third output, in combination with the second dynamic adapter adapter 130, forming a feedback path around the first dynamic adapter block 120.
A first output of the second dynamic adapter block 130 is fed back to a second input of the first dynamic adapter block 120. The output of the notch bandwidth determining block 170 is fed to a third input of the first dynamic adapter block 120.
A second output of the second dynamic adapter block 130 is left unconnected. A third output of the second dynamic adapter block 130 is fed back to a second input of the second dynamic adapter block 130. The output of the notch frequency determining block 180 is fed to a third input of the second dynamic adapter block 130.
FIG. 2 shows a block diagram showing functional elements for implementing the dynamic adapters 120 and 130.
In FIG. 2, there is shown a first input 210, a second input 220, a third input 230, a first subtracter block 240, a multiplier 250, a second subtracter block 260, a third subtracter block 270, a delay block 280, a first output 285, a second output 290 and a third output 295.
The first input 210 is fed to the positive input terminal of the first subtracter block 240 and to the negative input terminal of the third subtracter block 270. A second input 220 is fed to the negative input terminal of the first subtracter block 240 and the negative input terminal of the second subtracter block 260. The output of the first subtracter block 240, comprising the difference of the first input 210 and the second input 220, is fed to a first input terminal of the multiplier 250. A third input 230 is fed to a second input terminal of the multiplier 250. The output of the multiplier 250, comprising the product of the third input 230 and the output of the first subtracter block 240, is fed to the positive input terminal of the second subtracter block 260 and to the positive input terminal of the third subtracter block 270. The output of the second subtracter block 260, comprising the difference of the output of the multiplier block 250 and the second input 220, becomes the first output 285. The output of the third subtracter block 270, comprising the difference of the output of the multiplier 260 and the first input 210, becomes the second output 290 and is also fed to the delay block 280. The delay block 280 delays the signal by one sample period then feeds it to the third output 295.
The time domain response of the dynamic adapter can be evaluated. From an initial state where the values of all inputs and outputs are zero, a train of pulses a1, a2, . . . , an, an+1, . . . is applied to the first input 210, a train of pulses b1, b2, . . . ,bn, bn+1, . . . is applied to the second input 220, and the constant K is applied to the third input 230. Then the outputs at the nth time step become:First output 285 (an−bn) X K−bnSecond output 290 (an−bn) X K−anThird output 295 (an−1−bn−1) X K−an−1
The time domain response of the dynamic adapter, shown in feedback configuration in FIG. 5 (and in the dashed box in FIG. 1), can be evaluated. From an initial state where the values of all inputs and outputs are zero, when a train of pulses u(1), u(2), . . . ,u(n), u(n+1), . . . is applied to the input 510 and the constant K (520) is applied to third input of dynamic adapter block 530, the equation for the output 540 at the nth time step becomes:Output 540y(n)=K×u(n)+u(n−1)−K×y(n−1)
This corresponds to an all-pass transfer function in the z-transform domain of       H    adaptor    =            K      +              z                  -          1                            1      +              Kz                  -          1                    
It is desirable to reduce the computational complexity of ALEs.